Sklar's Theorem and Quantum State Reconstruction from All-Context Dependence

• URL: http://arxiv.org/abs/2609.08035v1
• Date: Mon, 07 Sep 2026 22:43:27 GMT
• Title: Sklar's Theorem and Quantum State Reconstruction from All-Context Dependence
• Abstract summary: We apply Sklar's theorem to Born statistics generated by local quantum measurements.<n>For non-product two-qubit states, the dependence nuclei over all local binary projective measurement contexts determine the state up to at most a discrete double-spin-flip ambiguity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sklar's theorem separates the marginals of a joint distribution from its dependence structure. We apply this viewpoint to Born statistics generated by local quantum measurements. For non-product two-qubit states, the dependence nuclei over all local binary projective measurement contexts determine the state up to at most a discrete double-spin-flip ambiguity. The corresponding scalar optimization, combined with the quantum total correlation, reproduces global quantum discord.

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